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2016-09-30
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Rotella Capital Management, Inc.

CTA Performance During the Brexit Vote

On June 23, 2016, the UK electorate voted 51.9% in support of an exit from the European Union. This resulted in significant market turmoil over the following trade day. The voting outcome came as a surprise to many, who saw the exit as unlikely. Perhaps more surprisingly, medium- to long-term trend followers benefited from the announcement: the SG CTA Index increased 2.27%. Why? Were CTAs forecasting the event?

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Qualitative examination of price movements suggests that markets were trending in the direction of the Brexit exit in the prior months. This is supported by systematic analysis over the same period. There are many ways to define the concept of “trend,” and while it is useful to visually examine the evolution of prices themselves over time, creating a trend metric has its own utility in terms of creating a less subjective view of market behavior. Signal-to-noise ratio (SNR), which attempts to quantify the strength of a price trend by looking at how uniformly it increases or decreases, is one such measure.

In terms of its computation, the SNR is simply the absolute price change over the lookback period divided by the sum of the absolute daily price changes. The lookback period of choice depends on the timeframe of interest. For medium- to long-term trend followers that can mean anywhere from 40 to 120 days. The closer the price path is to a straight line over that period, the higher the SNR. A perfectly straight line will have an SNR of 1, while a completely flat path will have an SNR of 0. Below are some examples with generated data.

 

For the purpose of the analysis in this article, we also are interested in the direction of trends and not merely the strength, so in this context a sign is applied to SNR: positive for when the price increases over the lookback period and negative otherwise.

In addition to the SNR, the net positions of a simple trend following system are included in our analysis. While the details of the system are beyond the scope of this article, for the most part these positions are in the direction of longer term price movements, and are not immediately responsive to shorter term rebounds and whipsaws. The entry points of this system’s positions line up closely with the SNR observed on those dates. In the following charts the roll-adjusted price of a representative set of futures contracts is plotted, along with SNR over several timeframes and the net position of the sample system. From this we can hopefully determine why CTAs benefited from Brexit.

 

 

Gold exhibited some choppy behavior characterized by changing dynamics. 2014-2015 resulted in a weak negative trend, followed by a strong reversal in 2016. This led to higher magnitude SNR values than seen in other commodities, sufficient enough to bring the net position of our sample system into positive territory. This rebound likely benefitted CTAs when gold appreciated 4.69%.

 

 

European equities, and to a lesser extent global equities, exhibited weak downward trends in the later part of 2015. The recent recovery boosted SNR in multiple timeframes, but long-term trend followers likely retained short equity exposure because of their longer lookback period. The Euro STOXX 50 did not rebound to the same extent as some other indices. Because of this signal it is probable that CTAs had mixed exposure going into Friday the 24th, but biased on the short side. FTSE 100 and Euro STOXX 50 depreciated -8.56% and -2.90% respectively that day, so a correctly timed position would have paid off significantly.

With currencies the story was more clear cut. The Yen appreciated this year relative to the US Dollar, after a flat period characterized by a low SNR in most of 2015. This resulted in moderately high positive SNR values and long positioning of the sample system. The British Pound has been weakening fairly consistently, and this also is true year-to-date. Both of these currency futures moved in the direction of their year-to-date trend.

 

Bond futures have been in an extended bull market. This is especially apparent from mid-2015 onwards. This is reflected by above average, positive SNR values over the same period. Bond prices rose sharply, with the EUREX Euro-Bund increasing 1.24% and the CBOT 10-year note rising by 1.19%.

In the table below, we compare the sign of the 120-day SNR, at the time our sample trend following system entered its current position, to the direction of the move on Brexit. As expected, the direction and strength of the trend lines up with the trades the trend following system made. This supports the notion that, while CTAs were correctly positioned for Brexit, their exposure was dictated by trends that originated well prior to the actual event.

While it is tempting to claim that CTAs correctly predicted Brexit coming to fruition, it is more accurate to state that their positions simply reflect longer term trends in the futures contracts they trade. It is possible that as Brexit became more probable, the effect of its outcome became slowly reflected in market prices, resulting in the appearance of the aforementioned trends. This reasoning likely overstates the effect of a singular event. Regardless, SNR and simple qualitative analysis can shed light into the decisions made by CTAs and help to explain the effect of their stances during key events.

Rotella Capital Management anticipates the remainder of 2016 will occur as we describe, but note that unexpected events could change our outlook. We are still bullish on interest rates but this could be the last hurrah for a long time as we should be getting close to a secular bottom in interest rates. The dollar may rise and appear to be a temporary “safe haven.” Most commodities should continue on the deflationary path except for the metals which should continue to rise. Though we are still long-term bullish on stocks the equity markets may encounter strong headwinds in the next 6 months and we are neutral to bearish.

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2015-10-19
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Categories: Blog, Newsletters
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By Robert Rotella, CEO, Rotella Capital Management, Inc.

Historical Analysis of CTA Performance in Q4: Relating Returns to Trends

One issue faced by fund managers is developing expectations for the future returns of their products. This task for CTAs is made more complicated by the fact that many strategies are designed to be uncorrelated to conventional market indices, benchmarks and indicators.

An approach to generating such a forecast is to relate strategy returns to bespoke factors that pertain to the known characteristics of the strategy (e.g., trend following or mean reversion). If some of these factors can themselves be predicted with accuracy, then in principal that prediction can be extrapolated to the returns of the strategy.

While CTA returns tend to be uncorrelated to commonly used factors (such as Fama-French factors), it is possible to follow this approach and define custom indicators that have explanatory value. An example of this is a market trend index: if markets exhibit strong, persisting trends, one would expect trend following CTAs to perform well. If trends are weak or nonexistent, trend following CTAs ought to have flat or negative performance. This effect can be measured quantitatively.

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There are many ways to define the concept of “trend.” A market trend index is one possible approach, which happens to be a useful explanatory factor for CTA (as defined by the Newedge CTA index) performance. The first step in computing the market trend index is to calculate a signal to noise ratio (SNR) for asset prices over a given lookback period. The SNR is simply the absolute price change over the lookback period divided by the sum of the absolute daily price changes. The lookback period may vary depending on the length of trends of interest, but two months or longer tends to relate sufficiently closely to CTA returns in terms of linear correlation to a benchmark index. The closer the price path is to a straight line, the higher the SNR. A perfectly straight line will have an SNR of 1, while a completely flat path will have an SNR of 0. Below are some examples with generated data:

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In the second step to computing the market trend index, the SNR for individual futures is aggregated into an index by taking the relevant average. For example, the equity sector trend index is the average of the SNR for equity futures such as the Dow Jones Industrial Average, S&P 500 E-Mini, Eurex DAX 30 and the FTSE 100. An overall trend index would be the average among all tradable markets.

Because this market trend index is a measure of how “trendy” futures prices are, we expect it to correlate with CTA trend follower performance over comparable time frames. Below is a plot of the Newedge CTA index quarterly returns (blue) alongside the SNR trend index (red) computed for the same period:

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The correlation between these two series is 62%.  Below the same data are depicted in scatterplot form.

clip_image006Notice the clustering of points around the regression line.
Given this quantitative definition of the level of trend, statistical tests can be performed to examine whether there are consistent patterns in the level of trend.
One question we hope to address using the SNR is how fourth quarter trends compare to the remainder of the year, on both a sector and overall level for futures. We can start by examining the SNR of a representative set of futures contracts from four different sectors (equity indices, commodities, currencies, and interest rates) from 1990 onwards. The average SNR from Q4 can be compared to the average SNR from quarters 1-3 by using a paired Student’s T-test. The null hypothesis of Q4 SNR equaling Q1-3 SNR is rejected in favor of the alternative that Q4 SNR is greater at the 10% level (p-value = 0.090, t=1.37). While this level of significance may only be modest, it does suggest that, at the very least, the trendiness of all quarters is not necessarily uniform.

To take this analysis a step further, we form sector-level SNR indices, which are the individual futures’ SNR indices averaged at the sector level. Since there are only 4 sectors we compare the values of Q4 SNR to the values of Q1-Q3 SNR. This results in an unequal sample size (25 observations for Q4 PL, 75 for Q1-Q3 PL), necessitating a Welch Two Sample T-test. However, this test has the unfortunate consequence of assuming that each sample follows a Gaussian distribution, but quarterly SNR fails a Jarque-Bera test for normality. Regardless, the following t-test might give some insight into the source of the differing Q4 SNR.

Sector

Less than Q1-Q3

Greater than Q1-Q3

Not Equal to Q1-Q3

Commodity

95.72%

4.28%

8.57%

Currency

50.14%

49.86%

99.72%

Equity

63.12%

36.88%

73.76%

Interest Rate

36.98%

63.02%

73.97%

Above: p-values for Q4 sector SNR when compared to Q1-Q3 (smaller is more significant)

Referring to the above table of p-values, we find that only one sector deviates at the 10% level in Q4 from the remainder of the year. Commodities tended to have stronger trends in Q4.

If this Q4 effect on trends exists, and if CTA returns relate positively to the trend index, we should also expect to see higher than average CTA returns in Q4. We can perform the same t-test on Newedge CTA index quarterly returns. The null hypothesis that Newedge CTA Q4 returns have the same mean as Q1-Q3 is rejected in favor of the alternative that Q4 is greater at the 1% level (p-value = 0.00135, t=3.17). The average annualized return in Q4 was 14.4% vs. 2.67% in the remaining quarters. This effect is also apparent in other CTA indices, namely the Newedge CTA Trend Index, which has an even starker difference at 22.7% annualized in Q4 vs. 2.6% in the remaining quarters.

The available evidence suggests that commodity trends tend to be much stronger in Q4, possibly leading CTAs to perform much better than average during this period. In future research it may be worthwhile investigating what contributes to these Q4 trends (perhaps relatively low volatility or seasonal effects reflected in prices), as well as how to incorporate this information in the systems underlying a CTA strategy.

Relating SNR to CTA Crisis Alpha

One appealing characteristic of CTAs is their performance under periods of market distress, or crisis. If we flag periods as crises using the following criterion: S&P 500 Index monthly returns below their 10% quantile (-4.7%), we observe that the Newedge CTA index realized an annual return of 19.5% in these months, compared to 3.3% in non-crisis periods. Based on the previous analysis, it is possible that this crisis alpha is in part driven by an increase in the level of trend in markets (e.g. downward trend in the case of the equity markets). If CTAs can exploit the persistence of such trends in a crisis, they stand to benefit from prolonged downturns.

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Distribution of monthly S&P 500 Index returns with a dotted line depicting the 10% quantile. Crisis periods depicted in red.

A similar crisis alpha effect exists with respect to other stock market indices. For example, let us consider the Korea Composite Stock Price Index. Flagging crisis periods using the 10% quantile of monthly returns yields a value of -7.3%. Crisis periods for the KOSPI in red.

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The Newedge CTA Index realized an annualized return of 9.5% in these crisis periods, vs. 4.9% in non-crisis periods. Crisis alpha appears robust to the equity index used.

Returning to the S&P 500, we may be able to gain insight into the source of crisis alpha by examining how the aggregate level of trend, measured by average SNR, changes during crises. Applying a Welch Two Sample T-test comparing crisis aggregate SNR values to observations from the rest of the sample (1990 onwards), we find that we may reject the null hypothesis that the two samples have equal mean in favor of the alternative that crisis SNR is greater at the 5% significance level (p-value = 0.042, t=1.79).

We may apply the same test at the sector level to see if a subset of futures markets are trendier during these periods. Below is a table of the p-values from this test:

Sector

Less Trend in Crisis

Greater Trend in Crisis

Commodity

54.41%

45.59%

Currency

91.89%

8.11%

Equity

69.32%

30.68%

Interest Rate

98.29%

1.71%

Above: p-values for comparing sector SNR in crisis periods to non-crisis periods in the S&P 500 Index

 

Contrary to the assumption that successfully exploited equity market trends are the source of crisis alpha from CTAs, equity trends as measured by SNR do not appear to differ at the 10% significance level. However, interest rate trends, and to a lesser extent currency trends, deviate from their non-crisis levels. This may be because equity downturns are preceded by persisting trends in these other sectors that are followed accurately. While the understanding of the source of CTAs’ crisis alpha remains incomplete, SNR provides some insight into market behavior during these events.

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2015-08-14
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Categories: Blog
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The Relationship Between Bonds And Equities

The surface examines the relationship between bonds and equities over time. In particular, the pre- and post- crash behavior contains useful information as it diverges from what might be considered the normal regime.

The plot depicts normalized intraday price returns between US 10-year note futures and E-mini S&P 500 futures for 2 months at a time. A representative sample of the returns is used, and these are normalized by taking their rank over each period.

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As volatility increases, we can see that the surface warps as returns are drawn to their relative extremes in the corners of the surface. Volatility dynamics along with changes in the bond-equity relationship interact to form rich surface characteristics.

A consequence of using intraday returns is that in high volatility periods returns will typically not be near the median, depicted by the center of the surface. Instead clusters tend to appear in the surface along the diagonals, either showing positive association where stocks are moving in the same direction as bonds, or the reverse.

From 1997 through 1998, the relationship is initially a weak one, with returns occupying each of the four quadrants. Late 1998 sees returns drawn to each of their respective extremes until early 1999, forming a diagonal. This period corresponds to a spike in equity volatility.

In late 1999 another diagonal appears, this time in the opposite direction, representing the less common positive association between bond and stock returns. 2000 then sees a less sharp diagonal and consolidation towards the median. The diagonal becomes stronger in mid-2001, persisting but in a weaker state until 2002 when it periodically strengthens. From 2004 through mid-2007, a consolidation towards the median occurs in both asset classes, but with weak positive association sporadically appearing.

Beginning in September 2007, a strong negative relationship appears as equities begin their downward spiral and bond yields decline. Wide swings occur in equities along with bonds, reducing the concentration along the diagonal as the market crashes in the following year.

The diagonal reappears in 2012, almost immediately following the high volatility period in August 2011 that continued for the remainder of that year. Finally, once we reach the post-crash period in 2012, the surface consolidates towards the center as tail events diminish further. This reduction in volatility continues to persist until the beginning of the recent China stock market crash.

The relationship between stock and bond price returns is related to investor risk aversion. In crisis periods, as stocks decline investors are drawn to assets perceived as safer. This results in bond prices increasing, and yields decreasing. For this reason the high volatility periods correspond to a negatively associated diagonal line in the surface. Recognition of prevailing market conditions is of paramount importance when engaging in investment, both in terms of risk management and timing.

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2015-05-07
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Categories: Blog
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Market Trend Barometer

The Trend Barometer measures the percentage of markets with medium to strong trends. Just as a thermometer reading of 32 degrees Fahrenheit equates to freezing, when the Trend Barometer reads a value that is less than 40%, market trendiness begins to get “colder” or weaken. Likewise, when the Trend Barometer gets “hotter”—that is, moves above 45% — the more markets are trending.

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There are many ways to define the concept of “trend.” The market trend index is one possible approach, which happens to be a useful explanatory factor for CTA performance. The first step in computing the market trend index is to calculate a signal to noise ratio (SNR) for asset prices over a given lookback period. The SNR is simply the absolute price change over the lookback period divided by the sum of the absolute daily price changes. For a short term trend index, a period of 10 days is used. The medium and long term indices use 40 and 80 days respectively. The closer the price path is to a straight line, the higher the SNR. A perfectly straight line will have an SNR of 1, while a completely flat path will have an SNR of 0. Below are some examples with generated data:

imageimageimage

 

In the second step, the SNR for individual futures is aggregated into an index by taking the relevant average. For example, the equity sector trend index is the average of the SNR for equity futures such as the Dow Jones Industrial Average, S&P 500 E-Mini, Eurex DAX 30 and the FTSE 100. An overall trend index would be the average among all tradable markets.

Because this market trend index is a measure of how “trendy” futures prices are, it tends to be correlated with CTA trend-follower performance over comparable time frames. Below is a plot of the NewEdge CTA index 40 day returns alongside the trend index computed for the same period:

image

The correlation between these two series is 56% (R2=75%).

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